Here is some of the latest on how Classic physics and Quantum Physics allow the existence of free energy cold fusion and Anti Gravity
The first link leads on to a total of 23 parts which you find yourself as I dont do 23 links
Enjoy all cliff hanging stuff

Anti-Gravity / Cold Fusion Explained In Detail: A New Era In Physics Pt. 1 of ?

Yeah well the jury is still out with E CAT
However what the you tube series here explains mathematically how they can make Nickel metal turn into copper metal without using as much power as the normal laws of Physics would require

However although the physics say its looking possible for the E CAT to work I remain unimpressed with E CAT obscuration of its mathematics at any level

However there was last year one Canadian on TV show who raised $1,000,000 from the investors (Dragons ) who showed his invention a machine that takes one kilowatt and returns many more kilowatts. Thats called overunity .
One Investor saw his chance and put money where his mouth was and invested $1,000,000 into the project

The entire series explains using mathematics that at no time does free energy break the First law of thermodynamics
Best example of this perpetual motion is nature is chock a block full of perpetual energy in the form of the electron that orbits the nucleus in a atom. For the electron to remain in orbit (forever short of destroying the atom )that in itself is in your face solid proof of the existence of perpetual motion .They also have the mathematics to explain why that is so and how to tap into this power source and even with transmutation make hydrogen into Helium at room temperature